Answer:
f(x) = 4x - 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 1) and (x₂, y₂ ) = (2, 5) ← 2 ordered pairs from the table
m = [tex]\frac{5-1}{2-1}[/tex] = 4 , thus
y = 4x + c ← is the partial equation
To find c substitute any ordered pair from the table into the partial equation
Using (2, 5) , then
5 = 8 + c ⇒ c = 5 - 8 = - 3
Thus
f(x) = 4x + 3 ← is the function rule
